C₅×D₂₀₃ #14523200

order	2030
isoclinism	isoclinic class of D₂₀₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₂₀₃
unambiguous semidirect product	C₇⋊(C₅×D₂₉)
unambiguous semidirect product	C₂₉⋊(C₅×D₇)

Splittings

Fitting, socle, Hall	C₅×C₇×C₂₉ ⋊ C₂
derived, Hall	C₇×C₂₉ ⋊ C₂×C₅
Hall	C₅×C₂₉ ⋊ D₇
Hall	C₅×C₇ ⋊ D₂₉
Sylow	C₂₉ ⋊ C₅×D₇
Sylow	C₇ ⋊ C₅×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅	D₂₀₃
commutator, cosocle, hypocenter	C₇×C₂₉	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₂₉	C₂
LCS	G ▷ C₇×C₂₉
UCS	C₁ ◁ C₅

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 1015

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3,4,5)(6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(7,12)(8,11)(9,10)(14,41)(15,40)(16,39)(17,38)(18,37)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)

Conjugacy classes & character table

515 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₇×D₂₉, D₅×D₂₀₃, D₃₅⋊D₂₉, …
maximal normal subgroup of	C₅×D₇×D₂₉, D₅×D₂₀₃, D₃₅⋊D₂₉, …
maximal quotient of	C₅×Dic₂₀₃, C₂×C₅×D₂₀₃, C₅×D₁₄₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2030, 5);

C5×D203 #14523200